Progress in the determination of Mellin moments of the pion LCDA using the HOPE method

Abstract

The pion light-cone distribution amplitude (LCDA) is a central non-perturbative object of interest for the calculation of high-energy exclusive processes in quantum chromodynamics. In this article, we discuss the calculation of the second and fourth Mellin moment of the pion LCDA using a heavy-quark operator product expansion. The resulting value for the second Mellin moment is ξ 2 (µ = 2 GeV) = 0.210 ± 0.013 (stat.) ± 0.034 (sys.). This result is compatible with those from previous determinations of this quantity.

Progress in calculation of the fourth Mellin moment of the pion light-cone distribution amplitude using the HOPE method

“…(8). In order to extract R µν 1 from lattice data, which in general contains additional terms from excited-state contamination, previous studies [11,[13][14][15] compute the above three-point correlator at large Euclidean time, and then construct the ratio C…”

“…[4] and expanded on in Refs. [11][12][13][14][15]. The method relates hadronic matrix elements directly computable in Euclidean field theory to a heavy-quark operator product expansion (HOPE), where the non-perturbative information about the LCDA is encoded in its Mellin moments that can be determined by fitting lattice data to the HOPE.…”